Subspace design code[1,2] 

Also known as \(q\)-design code, Geometric design code.

Description

A \(q\)-ary code that can be mapped into a subspace \(t\)-\((n,w,\lambda)_q\) design.

Subspace designs exist for all parameters in sufficiently large dimension that also satisfied divisibility constraints [3].

Notes

See [4] for a review on subspace designs.Popular summary of the existence of subspace designs in Quanta Magazine.

Parent

Child

References

[1]
Cameron, Peter J. "Generalisation of Fisher’s inequality to fields with more than one element." Combinatorics, London Math. Soc. Lecture Note Ser 13 (1973): 9-13.
[2]
V. Guruswami and C. Xing, “List decoding reed-solomon, algebraic-geometric, and gabidulin subcodes up to the singleton bound”, Proceedings of the forty-fifth annual ACM symposium on Theory of Computing (2013) DOI
[3]
P. Keevash, A. Sah, and M. Sawhney, “The existence of subspace designs”, (2023) arXiv:2212.00870
[4]
M. Braun, M. Kiermaier, and A. Wassermann, “q-Analogs of Designs: Subspace Designs”, Network Coding and Subspace Designs 171 (2018) DOI
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Zoo Code ID: subspace_design

Cite as:
“Subspace design code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/subspace_design
BibTeX:
@incollection{eczoo_subspace_design, title={Subspace design code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/subspace_design} }
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Cite as:

“Subspace design code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/subspace_design

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/subspace_design.yml.